Interactive module

Split Rent Fairly

Use sealed bids to turn messy room preferences into adjusted rents.

Rule ledger

caseThree roommates rent a $1600 apartment with rooms that feel valuable for different reasons.

rulerent_i = value_i(assigned room) - (total assigned value - total rent) / n

questionWhen one strategy changes alone, whose payoff or fairness changes first?

Sealed-Bid Room Split

RoommatesOffice desksShared studios

Large Room

Floor-to-ceiling window

Assigned to

Ava

Rent $640

Medium Room

1.8m bed and balanced light

Assigned to

Ben

Rent $490

Small Room

Quiet, no window view

Assigned to

Chloe

Rent $470

Roommate	Large Room	Medium Room	Small Room
Ava
Ben
Chloe

Ava surplus

$120

Ben surplus

$120

Chloe surplus

$120

How to read this result

First assign rooms to the strongest valuations, then adjust rents back to the $1600 total. Equal surplus means nobody is left with a worse deal by their own bids.

Formula

rent_i = value_i(assigned room) - (total assigned value - total rent) / n

Everyone gets the same surplus after the assignment, so the person who values a room more pays more.

Step-by-step Explanation

Scenario

Three roommates rent a $1600 apartment with rooms that feel valuable for different reasons.

Why This Matters

A fair division rule can replace awkward negotiation with a transparent process.

Beginner-Friendly Summary

Bid honestly, assign rooms by strongest fit, then adjust prices so every roommate keeps equal surplus.

Try changing the strategy and watch which result changes first.